Logs found on my computer

I have no idea what is in Preboot. It should not be mounted normally, so I'm not sure how you are seeing it in the first place. The volume is required for booting from APFS drive, but other than that, it doesn't do anything after boot as far as I'm aware.

Log files are useless, for the most part. There is nothing user-usable in them. Only the developer of the software posting the log entry can decipher the logs. The only value might be large chunks of the same log entry repeating thousands of time (but we don't need to see thousands of identical entries). That might give a clue as to what is hanging the system, but even then nobody but the developer could interpret why it is happening.

What model/year Mac is it? Does it have a T2 chip? If so, did you enable external booting in the Secure Boot settings?

If not a T2, is the external drive connected directly into a port on the Mac and not through a hub?

You could spend a lot of time trying to hunt down the source of the problems you are seeing, or you could erase and reinstall. I've never spent more than about four hours erasing and reinstalling the OS, usually less. It will take a while to download the installer, but you can be using the computer during that time.

I would erase the drive completely and reinstall the OS. Then, before migrating anything, I would make sure it seems to work normally.

Then I would migrate only my user data from a backup. Reinstall only the apps you need from scratch.

Make sure you have a backup (or two). A bootable clone is handy to have as one of the backups. I think Carbon Copy Cloner can now make a bootable Big Sur clone.

To erase the drive completely, boot into Internet Recovery or use a bootable USB installer. I think the USB installer is safer as you have an installer to work from if Internet Recovery cannot connect to Apple's servers. However, if you cannot resolve the external boot issue, this might not be possible.

In Disk Utility, Show All Devices from the View button in the toolbar.

Select the drive device which should be at the top of the list. It will be named by using some combination of model/manufacturer/size

Erase that using APFS format.

Then, Quit Disk Utility and reinstall the OS.

Once installed, create a new user account that is not an account you will migrate later on.

Set up enough services (email, iCloud, etc.) to ensure it works correctly. If it all seems to function normally, use Migration Assistant to migrate your user from your backup. In Users & Groups, you can set up your old account to Administer the computer or not and just use that account you created as an admin account.